Main Problem
Noise attributable to innate characteristics of photographic film limits the quality of images obtainable from photographic film. The major source of such noise is random variations in the density of silver halide grains across the surface of a film emulsion layer. If the film is divided into many picture elements ("pixels") which are sampled individually, each pixel will have a different number of silver halide grains. Such random variations in the number of silver halide grains in each "pixel" on the film causes different pixels to respond differently to the same incident light. Upon chemical development, pixels with more grains develop higher dye densities. These pixel-by-pixel variations in density appear as granularity. This can be thought of as random pixel-to-pixel variations in sensitivity--pixels with more grains are more sensitive, having a higher response to the same incident light.
However, by independently developing and digitally scanning both latent and non-latent silver halide grains in each pixel, the total number of grains in each pixel can be determined. Using this information, the random variations in the number of grains per pixel on film may be compensated by simply normalizing or dividing the number of latent (or non-latent) grains counted in a given pixel by the total number of latent and non-latent grains in that pixel.
Typically, using a single dye (positive or negative), scanning the film yields either the number of non-latent grains or the number of latent grains in each pixel, but not both numbers. In order to obtain both numbers, two different color dye are used, one dye responsive only to the non-latent grains and the other dye responsive only to the latent grains. By developing the same film with both dyes, and by scanning the film with two different color filters tuned individually to each of the two dyes, the scanner can separately count the number of latent and non-latent crystals in the film. Such a process is described in detail by Bird, "Normal Development, Reversal Development, and Composite Processing: A New Method for Gaining a Simultaneous Improvement in Latitude and Detective Quantum Efficiency in Silver Halide Films," Photographic Science and Engineering, Vol. 22, No. 6, pages 328-335, November/December, 1978 (hereinafter referred to as "Bird"). The Bird reference proposes an algorithm for combining the densities of D.sub.n and D.sub.p by individually weighting them and then computing the exposure from the combination. The Bird algorithm optimizes the detective quantum efficiency (the ratio between the input noise and the output noise of the process) requiring certain assumptions in film characteristics, the main assumption being an idealized monodisperse emulsion in the film. This assumption means that the silver halide grains are of identical size throughout the emulsion so that each grain: (1) presents the same photon absorption cross-section "area", (2) requires the same number of photons in order to become latent, (3) lies at the same height as all other grains in the emulsion so as not to obscure one another, and (4) produces the same amount of dye.